Re: upper and lower bounds as constraints?
- From: "Max Touzel" <mtouzel@xxxxxxxxxxx>
- Date: Tue, 11 Apr 2006 23:29:07 -0400
Excuse the spelling mistakes in the above! I neglected to say that
the optimization is also over the weights mentioned in the beginning
(which gives the quadratic dependence I was talking about).
Thanks
Max
Max Touzel wrote:
.
Hello,
I have a question regarding mor efficient optimizations. Here is
the
scenario:
The objective function is a sum of quantum probabilities given as
the
square of the inner product of vectors. Each term is multiplied by
a
weight between 0 and 1. THere is 1 equality constraint of similar
form. In the inner products, one vecotr is input the other is part
of
the optimization variable. I had originally expressed them in euler
angles. I've been thinking about doing it in straight components
instead. This makes the above two expressions(1 objective and 1
constraint) quadratic, which is
good. However, it adds 6 nonlinear equality constraints: 3 unit
length and 3 mutual orthogonality conditions, which are also
quadratic (and were implicitly satisfied in the euler
parametrization). So, which is likely to be more efficient: 7
quadratic constraints and 1 quadratic objective function, or 1
objective function and 1 constraint both with sines and cosines?
This
may be related to a more general question: is there any general
advice on whether to put 'the difficulty' of your problem in the
constraints or in the objective function? This is broad, I know,
but
any advice would be appreciated.
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- From: Max Touzel
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